Generalized (edge-)connectivity of join, corona and cluster graphs

The generalized k-connectivity kappa(k)(G) of a graph G, introduced by Hager in 1985, is a natural generalization of the classical connectivity. As a natural counterpart, Li et al. proposed the concept of generalized k-edge-connectivity lambda(k)(G). In this paper, we obtain exact values or sharp upper and lower bounds of kappa(k)(G) and lambda(k)(G) for join, corona and cluster graphs.